This question aims to find the practical and **statistical significance** of the** difference in percentages** of two different populations. In the **1950s**, the population of the **US** amounted to **151.3 million** persons and **13.4 %** of them were living in the West according to census data. This population percentage increased to **281.4 million** and 22.5 % of them were living in the West in the year** 2000.**

If we gather the percentage of the population living in the West then we come to know that, only **13.4%** of the total population of the US was living in the **West** in the **1950s** while this percentage increased to **22.5%** of the total population in **2000.**

We can find significance by applying two sample z-test. It is the **hypothetical testing** of the statistical data of two samples to determine that the **mean of the difference** between** two populations** is not statistically significant. Knowing the standard deviation of two populations is an important tool for applying this test.

## Expert Answer

If we take the **difference** between both percentages, we can easily tell the increase in population over **50 years.**

\[Difference = 22.5 – 13.4\]

\[Difference = 9.1\]

**9.1%** is a large difference in percentages, which means the difference in percentages is partially significant.

To check whether the difference is **statistically significant**, two sample z-test is conducted. This test is only useful to check significance when the given samples are **simple random samples.**

If every sample from the samples of **size n** has an equal probability of being chosen, then this is called **random sampling**. It is the best way of making **inferences** about statistical data. It helps to make an **unbiased choice** among the large population.

According to the given data, each individual among the population is representing a sample which means samples are not simple random samples. Therefore, it is not appropriate to find the statistical significance of the difference.

## Numerical Results

The samples are not probability samples, so it is not possible to determine whether the difference in percentages is statistically significant or not.

**The statistical significance of the difference in population percentages cannot be determined.**

## Example

The **population of Asia** increased from **3.1 billion** in the **1990s** to **4.7 billion** in **2018**. **17%** of the population of Asia was living in the **South** in the 1990s while **25%** population started to live in the South side in 2018. Find the **statistical significance** of the difference in population.

To find the statistical significance of the difference in population by using **two sample z-test**.

If we take the difference between both percentages, we can easily tell the increase in population from the 1990s to 2018.

\[Difference=25 – 17\]

\[Difference = 8\]

The difference in population is **8%.**

Since the individuals represent samples of the population that means the samples are not simple random samples.

**The statistical significance of these samples cannot be determined.**

*Image/Mathematical drawings are created in Geogebra**. *